The historic marks that identify the visible church of Jesus Christ are the pure preaching of God's Word, the right administration of the sacraments, and the faithful practice of church discipline (see here for an explanation as to why these three marks). This trinity of distinguishing traits of what constitutes a true congregation of God's people are dependent on one another. Remove one, and the others will quickly become corrupted and disappear. Francis Turretin in his Institutes of Elenctic Theology says these marks are "necessary and essential" to the church like smoke is to fire or breathing is to life, and as such come "from the essence of the thing or from its inseparable properties" (Turretin 18.12.2).
Consider then the interdependence of the marks on one another.
Preaching and the Sacraments - When the sacraments of baptism and the Lord's Supper are observed by the church, they must be accompanied by the Word of God. Without preaching, the sacraments will not have their proper meaning and the partakers will not receive the benefits conferred by participating in them. For the sacraments are founded and depend upon the preaching of the Scriptures. The Westminster Confession of Faith states,
Sacraments are holy signs and seals of the covenant of grace, immediately instituted by God, to represent Christ, and his benefits; and to confirm our interest in him: as also, to put a visible difference between those that belong unto the church, and the rest of the world; and solemnly to engage them to the service of God in Christ, according to his Word. (WCF 27.1; see Rom. 6:3-4; Gal. 3:27; 1 Pet. 3:21; 1 Cor. 10:16)
The Confession goes on to say that grace received in the sacraments comes through "the work of the Spirit, and the word of institution" (WCF 21.3; see 1 Cor. 12:13; Matt. 26:26-28), and as such are only to be administered "by a minister of the Word lawfully ordained" (WCF 21.4; see Matt. 28:19; 1 Cor. 11:20, 23; 1 Cor. 4:1; Eph. 4:11-12). So the sacraments need the Word of God to give them proper context and power in the life of God's people.
Also, the preached Word needs the "visible" word of the sacraments to give shape and identity to it. Jesus commanded the church in the Great Commission to make disciples by baptizing them in the name of the Triune God, then teaching them all that Christ has given to the church. So baptism forms the visible boundary of those who truly respond to the gospel and are to be considered followers of Christ. They are then further sanctified in holy obedience to the Word as they partake in the Lord's Supper with one another (1 Cor. 11:23-33).
Preaching and Discipline - God's people are not only to hear the word, but obey it (Jas. 1:22; John 14:21). Thus, a preacher is not only to make sure his congregation hears the word but is obeying it. The pastor and elders must work diligently in lovingly shepherding the flock to help them follow their Good Shepherd, even when it means addressing them personally about their sins. As Edward Donnelly says in reflecting on Richard Baxter's The Reformed Pastor,
In order to be a true preacher, a man must be a true pastor. We may recognize the centrality of preaching, but do we ever use this as an excuse for pastoral cowardice or indifference? Does the fact of having preached publicly against men’s sins absolve us from the responsibility of confronting them in their homes concerning those same sins?
Baxter goes on to say that a preacher who does not uphold the truths he preaches with active visitation and, when necessary, taking official church actions against sin is being lazy and unfaithful to his calling.
John Calvin leads us into considering the next correlation between the marks when he says,
We have laid down as distinguishing marks of the church the preaching of the Word and the observance of the sacraments. These can never exist without bringing forth fruit and prospering by God’s blessing...and no one is permitted to spurn its authority, flout its warnings, resist its counsels, or make light of its chastisements - much less to desert it and break its unity. (Calvin, Institutes, 4.1.10.)
The Sacraments and Discipline - Calvin's words make us think of what we call the most serious act of discipline the church can take, that of removing a person from the membership of the church - excommunication. The very word means "to place out of the communion" of the body. This action shows the negative correspondence between the sacraments and discipline. To permanently ban someone who was formerly baptized and participating in the Lord's Supper, because they have disobeyed in an ongoing, arrogant way the Word of God, demonstrates the inner connectivity between the Word, sacrament, and discipline.
On the positive side, the holiness represented by the cleansing of sins by the waters of baptism, along with the body and blood of the Lord symbolized with the bread and cup, is to be possessed by the one receiving these sacraments. His or her life as a disciple of Jesus is to reflect the truths the sacraments convey. Baptism is a sign and seal to the believer "of his ingrafting into Christ, of regeneration, of remission of sins, and of his giving up unto God, through Jesus Christ, to walk in newness of life" (WCF 28.1). The Lord's Supper, among other things, is to help believers in "their spiritual nourishment and growth in him, their further engagement in and to all duties which they owe unto him; and, to be a bond and pledge of their communion with him, and with each other" (WCF 28.1). Thus, participating in baptism and the Lord's Supper are great encouragements in the consecrated life of disciplined holiness believers are to lead.
Again we see how the marks are "inseparable properties"as Turretin said, ones that correspond, support, and nurture one another.
For further reading on this subject, see Hitting the Marks: Restoring the Essential Identity of the Church.