Motion Isolation
A mattress with excellent motion isolation is a huge benefit for most couples since one person's movements like tossing and turning can keep the other one awake. Memory foam mattresses perform better than other types in terms of motion isolation. The material and construction absorbs movement and hinders it from transferring across the bed.
Firmness & Feel
Firmness & Feel is the most important factor because nothing else really matters if you don't feel comfortable sleeping on the mattress. If you and your partner are completely different in heights and weights, then you may need different firmness level on each side. Some air beds offer adjustable comforts on each side which enable two sleepers to find their ideal level of firmness separately.
Sex & Support
Sex should be taken into consideration when purchasing a mattress for couples. The mattress should have good support to hold the weight of two people located in generally the same place on the mattress. Good bounce and response are also important for sex. Innerspring mattresses and some hybrid mattresses may offer a high degree of bounce.
For a more detailed guide to sex, see our best mattress for romance here.