Maybe a bit of a late response...
Square has invoicing features... I haven't really dug into it though. And as far as I know, you only pay when someone pays via credit card.
I was actually a beta tester for their invoicing service. At that point it was laughable from such a big company. Absolutely terrible. I looked at it recently and it's really not much better.
I actually forgot about this thread. A friend of mine let me know about
Wave. It's a free service and very slick. A good UI on the web and in the app. I've been really happy with it and have closed down my Freshbooks account.