With a joint mortgage it is common for each partner to cover their contribution of the monthly repayments with MPPI, although there is no stipulation to say that both partners have to have cover.
For example, it may be the case that one partner pays the whole monthly loan repayment and therefore cover is only needed for that partner.
With regards to Life Insurance, the insurers do not currently have any rules to say that both partners have to be covered but it is important to check that your mortgage lender does not have a stipulation that if either partner dies then the loan has to be repaid immediately.
If this stipulation is present, and you would have trouble making that repayment, then it may be worth covering both partners.
Although the primary focus here is on mortgage protection, when deciding who is going to be covered and for how much, it is important to also consider all the other monthly bills that need to be paid in addition to the mortgage.
With most MPPI insurers it is possible to cover up to 125% of your monthly repayment. If more needs to be covered then an Income Protection policy is worth considering.