Multi-material polymer scaffolds with multiscale pore architectures are characterized and tested with vascular and heart cells as part of a platform for replacing damaged heart muscle. Vascular and muscle scaffolds are constructed from a new material, poly(limonene thioether) (PLT32i), which meets the design criteria of slow biodegradability, elastomeric mechanical properties, and facile processing. The vascular-parenchymal interface is a poly(glycerol sebacate) (PGS) porous membrane that meets different criteria of rapid biodegradability, high oxygen permeance, and high porosity. A hierarchical architecture of primary (macroscale) and secondary (microscale) pores is created by casting the PLT32i prepolymer onto sintered spheres of poly(methyl methacrylate) (PMMA) within precisely patterned molds followed by photocuring, de-molding, and leaching out the PMMA. Prefabricated polymer templates are cellularized, assembled, and perfused in order to engineer spatially organized, contractile heart tissue. Structural and functional analyses show that the primary pores guide heart cell alignment and enable robust perfusion while the secondary pores increase heart cell retention and reduce polymer volume fraction.