The Invisibility spell states:
If the subject attacks directly, however, it immediately becomes visible
Who is the attacker when a familiar delivers a touch spell? The familiar, the spellcaster or both?
From the PFSRD:
Deliver Touch Spells (Su): If the master is 3rd level or higher, a familiar can deliver touch spells for him. If the master and the familiar are in contact at the time the master casts a touch spell, he can designate his familiar as the “toucher.” The familiar can then deliver the touch spell just as the master would. As usual, if the master casts another spell before the touch is delivered, the touch spell dissipates.
This ability does not specify that the familiar counts as its master for the purposes of making the attack, just that it delivers the touch spell with the same parameters that the master would use. As a result, the default assumption - that the familiar is another creature and is treated as such - takes effect.