Different inner and outer hash functions for NIST-recommended HMAC? The NIST recommended HMAC uses 

$$\operatorname{HMAC}_k(\mathrm{text}) = H_\mathrm{out}( (k \oplus \mathrm{opad}) \mathbin\| H_\mathrm{in}((k \oplus \mathrm{ipad}) \mathbin\| \mathrm{text}) )$$

Is it feasible to analyze the security and efficiency with different hash function implementations for $H_\mathrm{in}$ and $H_\mathrm{out}$ for a single instance?

I would like to know whether it makes sense to use different hash functions for the same HMAC.
You may want to take a look at the original HMAC paper by Bellare, Canetti and Krawczyk (1996), or at the new security proof by Bellare (2006).

As far as I can tell at a glance, there's nothing in either of these proofs that would actually rely on the inner and outer hash functions being the same function, as long as both of them satisfy the appropriate security properties.