Unless you want/are okay with the fish being eaten, no - mantis shrimp (Stomatopods) are generally very effective predators, so they're usually kept in a species only aquarium (meaning a tank just for the one mantis shrimp and nothing else).
I've only read up a little bit on the care for these guys, but they need a burrow (typically provided in the form of PVC pipe in our aquariums), meaty foods, and to be left alone when molting (they typically seal themselves into their burrows to molt).
If I recall correctly, they need a minimum size of 40 gallons (they're relatively big and messy eaters); they need some rocks and such to seal off their burrow (I believe the burrow is typically U-shaped); and (again, IIRC) they may or may not develop shell rot at least in part because of strong lighting (so weak/ambient lighting is typically recommended - the relationship between lighting and shell rot seems to be correlation rather than causation).
For more info, I'd recommend looking through the forum linked below:
A place to talk about everything Mantis Shrimp
www.reef2reef.com