Seagrasses are vital organisms in coastal waters, and the drastic demise of their population in the last decades has worrying implications for marine ecosystems. Spatial models for seagrass meadows provide a mathematical framework to study their dynamical processes and emergent collective behavior. These models are crucial to predict the response of seagrasses to different global warming scenarios, analyze the resilience of existing seagrass distributions, and optimize restoration strategies. In this article, we propose a model that includes interactions among different species based on the clonal growth of seagrasses. We present a theoretical analysis of the model considering the specific case of the seagrass-seaweed interaction between Cymodocea nodosa and Caulerpa prolifera. Our simulations successfully reproduce field observations of shoot densities in mixed meadows in the Ebro River Delta in the Mediterranean Sea. Besides, the proposed model allows us to investigate the possible underlying mechanisms that mediate the interaction among the two macrophytes.