Co-exploitation attacks on software vulnerabilities pose severe risks to enterprises, a threat that can be mitigated by analyzing heterogeneous and multimodal vulnerability data. Multimodal graph neural networks (MGNNs) are well-suited to integrate complementary signals across modalities, thereby improving attack-prediction accuracy. However, designing an effective MGNN architecture is challenging because it requires coordinating modality-specific components at each layer, which is infeasible through manual tuning. Genetic algorithm (GA)-based graph neural architecture search (GNAS) provides a natural solution, yet existing methods are confined to single modalities and overlook modality heterogeneity. To address this limitation, we propose a modality-aware cooperative co-evolutionary algorithm for multimodal graph neural architecture search, termed MACC-MGNAS. First, we develop a modality-aware cooperative co-evolution (MACC) framework under a divide-and-conquer paradigm: a coordinator partitions a global chromosome population into modality-specific gene groups, local workers evolve them independently, and the coordinator reassembles chromosomes for joint evaluation. This framework effectively captures modality heterogeneity ignored by single-modality GNAS. Second, we introduce a modality-aware dual-track surrogate (MADTS) method to reduce evaluation cost and accelerate local gene evolution. Third, we design a similarity-based population diversity indicator (SPDI) strategy to adaptively balance exploration and exploitation, thereby accelerating convergence and avoiding local optima. On a standard vulnerabilities co-exploitation (VulCE) dataset, MACC-MGNAS achieves an F1-score of 81.67% within only 3 GPU-hours, outperforming the state-of-the-art competitor by 8.7% F1 while reducing computation cost by 27%.