Commutativity of keyed hashes
For H1=H2 there are one-way functions with that property: $y = g^x \mod p$.

$ (g^{k_1})^{k_2} = g^{k_1 \cdot k_2} = (g^{k_2})^{k_1}$

This property is exploited by the Diffie-Hellman key exchange. One variation of DH used for password based authentication is SRP.

I strongly recommend to use an existing protocol, and not write your own. Implementing SRP is quite easy to get wrong. I'd just use SSL, either with a normal suite (such as ECDHE_RSA) sending the password in plain over that connection, or using a SRP suite(only supported by a few libs, such as GnuTLS).