A processable rubber composition contains a double cured fluorocarbon elastomer dispersed in a matrix of a thermoplastic polymeric material. The cured elastomer contains repeating units derived from one or more fluorine-containing monomers, and further contains low levels of a peroxide cure site that contains at least one of a C--Cl bond, a C--Br bond, a C--I bond, and an olefin. In one embodiment the matrix forms a continuous phase and the vulcanized elastomeric material is in the form of particles forming a non-continuous phase. In various embodiments, the processable compositions are thermally processed into molded articles that exhibit a high degree of base resistance, especially a high degree of resistance to degradation of physical properties upon exposure to fluids containing strong nucleophiles such as amines.