Artificial spin ice (ASI) are arrays on nanoscaled magnets that can serve both as models for frustration in atomic spin ice as well as for exploring new spin-wave-based strategies to transmit, process, and store information. Here, we exploit the intricate interplay of the magnetization dynamics of two dissimilar ferromagnetic metals arranged on complimentary lattice sites in a square ASI to effectively modulate the spin-wave properties. We show that the interaction between the two sublattices results in unique spectra attributed to each sublattice and we observe inter- and intra-lattice dynamics facilitated by the distinct magnetization properties of the two materials. The dynamic properties are systematically studied by angular-dependent broadband ferromagnetic resonance and confirmed by micromagnetic simulations. We show that the combination of materials with dissimilar magnetic properties enables the realization of a wide range of two-dimensional structures potentially opening the door to new concepts in nanomagnonics.