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.