You can do this if you add a third service provider to the mix: a LISP provider. LISP (the Locator/Identifier Separation Protocol) decouples the location where you are on the network (the IP addresses you get from ISPs that you connect to) from your own identity (the IP address(es) you get from the LISP provider).
So your internal network runs using the LISP IP address(es), and your 'normal' ISP connections are only used to make that network reachable from the rest of the world. As long as at least one connection is working your network is reachable. And if multiple connections are working you can choose to use them for fail-over or for load-sharing (or combinations thereof).
LISP is mostly implemented on Cisco equipment, but the Fritz!Box routers also support it in recent firmwares. The hardest part will be to find a local LISP provider. Because LISP is so new there are only a few of those in the world.
(full disclosure: I run such a LISP provider in The Netherlands, so this answer might be biassed. I think it is a very useful protocol for situations like this though.)