Most Murphy beds do not require a special mattress.  In fact, shy away from Murphy beds that can only use a mattress supplied by the company.  When that mattress needs replacing in 10 years, then what?

Look for a Murphy bed provider that can use any mattress, with the only restriction being the thickness.  It is common for the thickness limit to be around 11” so the cabinet can be narrow (typically 16” deep) and the unit can fit nicely into even a small room.  This 11” thickness usually means that some of today’s plush, pillow top mattresses will not work.  Rather, a standard “old school” style mattress is what works best.  Any brand is fine, even a memory-foam mattress works well, as long as it is less than 11” thick.  Remember, though, that if you are supplying your own mattress, be sure it is delivered in advance of your installation date so the installers can balance your mechanism for extremely easy operation.