Sadly, mixing Humalog and Humulin won't work. First, these are totally separate preparations, so even if they could be mixed, the end result would not be the combined action, rather it would be a distorted smudging of the action.
But the real thing is that Humalog is only recommended for mixing with NPH. Another good pharmacist resource provides a convenient summary of how different insulins may be mixed for injection and pump use. It seems that none of the three major insulin analogs can be mixed with R, they can only be mixed with NPH.
Unfortunately, the only way to get the action you seek is to do two separate injections.