SSL Mutual (Two-way) Authentication Load Balancing

Per the referenced article:

Mutual SSL provides the same things as SSL, with the addition of authentication and non-repudiation of the client authentication, using digital signatures

This in effect relates to client certificates. In any SSL negotiation the server's certificate is always presented, so mutual authentication would also require the client's certificate. Now in terms of the proxy layer, if you offload (and optionally re-encrypt) at the VIP, then you have two separate client-server SSL sessions: client side (client to F5 server) and server side: (F5 client to web server). If you don't decrypt, then you have a single tunneled SSL session between the client and web server.

So if you need to do mutual SSL on the client side of the proxy, that's pretty straight forward. If you need to do mutual SSL on the server side of the proxy, that too is possible (between the F5 client and web server). But if you need the client's certificate at the web server, your options are limited to tunneling and ProxySSL.