George Andrews and Mohamed El Bachraoui recently explored identities for two-color partitions (Andrews and Bachraoui (2024) On two-color partitions with odd smallest part). In particular, they studied the connection between two-colored partitions and overpartitions. Their proofs were analytical, but they also conjectured combinatorial proofs of their results. In this paper we use two-modular diagrams to give a combinatorial proof of their main result.