When Reformed teachers say that they believe in "the visible church," this concept typically carries with it the idea of formal visibility. Thus, organizations like Calvary Chapel or movements like the "house church" movement are often opposed on the grounds that they reject formal categories of the church, such as formal church membership. Oversight and teaching is done in an informal way. Reformed teachers often object that without formal membership there is no formal accountability. In their thinking, to truly be a member of the visible church, one must submit in formal membership to a visible body of elders in a formal church congregation. For this reason, many Reformed churches will deny communion to those who are not in formal membership in some established congregation, treating them as being outside the visible church.
And yet many of these same Reformed teachers see no problem with identifying the "one general church visible" not with any particular denomination but with the whole of the Reformed or evangelical Christian world. In their view, the one universal visible church consists of many denominations independent from each other, such as the OPC, the PCA, the RCUS, the RPCNA, etc. But here's the rub: If the "one general church visible" consists of all the denominations in the Reformed or evangelical Christian world, then there is no "one general church visible" in a formal sense. There are degrees of informal fellowship between the denominations, but there is no formal unity between the denominations making up one general formal body subject to mutually-binding councils. Such formal unity exists within each denomination (at least the presbyterian denominations), but not between the denominations. So if the "visible church" has intrinsically a formal dimension, as is implied in Reformed criticism of Calvary Chapel and the "house church" movements (informal fellowship not being considered enough to constitute the "visible church"), then the only possible conclusion is that these Reformed thinkers deny the existence of "one general church visible." Instead, they have only "several particular church visibles." (And those outside of the Reformed world who have a strong commitment to the idea of "one general church visible," like the Romanists, have noticed this inconsistency in modern Reformed thinking and often comment upon it.)
But this modern tendency to see the "visible church" as consisting of the entire world of evangelical or Reformed denominations is a perversion of classic Reformed thought, because it is a perversion of the historic presbyterian view of the nature of the church and of church government. In historic presbyterianism, there is indeed "one general church visible," and so denominational division between true de jure churches is rejected as unthinkable. When denominations are divided from each other, this implies a mutual rejection of each others' de jure legitimacy and authority as churches. There can still be an informal recognition of the Body of Christ de facto between denominations, but not the Body of Christ de jure.
For more, see here and here.
UPDATE 3/10/15: In the Amazon.com description of the recent Romanist apologetics book against Protestantism by Devin Rose entitled The Protestant's Dilemma, we read this description of Protestantism:
What if Protestantism were true? What if the Reformers really were heroes, the Bible the sole rule of faith, and Christ s [sic] Church just an invisible collection of loosely united believers?
Obviously, this shows once again the Romanist confusion over the what the Protestant doctrine of the church really is, a confusion made somewhat understandable by internal lack of clarity on the doctrine of the universality of the visible church within Reformed circles themselves these days, despite the clear testimony of the Reformed doctrinal standards that there is indeed one catholic visible church.
In the introductory statement from the editor in the most recent (March 2015) edition of Ordained Servant, a periodical for church officers in the Orthodox Presbyterian Church, the editor makes this comment (this edition of Ordained Servant is devoted to the doctrine of church membership):
The modern world privileges informality with the mistaken idea that the informal is more authentic. So the written rolls of church membership and the vows to affirm the commitment of membership are seen as being unspiritual. This is a nineteenth-century Romantic ideal, not a biblical one, but cultural pressures persist, and the less people pay attention to their Bibles the easier world-conformity becomes.
And yet the denominationalist attitude within many Reformed circles today commits this very error--it denies any formal visible catholic church, and leaves us with only a bunch of visible particular churches or groups of churches (denominations) which have no formal governmental expression of their unity.