We consider theoretically the perpendicular upper critical field ${H}_{c2}$(T) versus temperature T for a proximity multilayer structure consisting of two superconductors, a and b, whose critical temperatures obey ${T}_{\mathrm{ca}}$g${T}_{\mathrm{cb}}$ but whose intrinsic upper critical fields obey ${H}_{c2a}$(0)${H}_{c2b}$(0). The latter condition can be satisfied if metal b is sufficiently dirty while metal a is relatively clean. The system's phase boundary, ${H}_{c2}$ versus T, may have a large positive curvature in the temperature domain where ${H}_{c2a}$(T)\ensuremath{\approxeq}${H}_{c2b}$(T). This curvature becomes sharper with increasing thickness.