Multimodal embedding models, built upon causal Vision Language Models (VLMs), have shown promise in various tasks. However, current approaches face three limitations: causal attention in VLM backbones is suboptimal for embedding tasks; scalability issues due to reliance on high-quality labeled paired data for contrastive learning; and limited diversity in training objectives and data. To address these issues, we propose MoCa, a two-stage framework for transforming pre-trained VLMs into bidirectional multimodal embedding models. The first stage, Modality-aware Continual Pre-training, introduces a joint reconstruction objective that simultaneously denoises interleaved texts and images, enhancing bidirectional context-aware reasoning. The second stage, Heterogeneous Contrastive Fine-tuning, leverages diverse, semantically rich multimodal data beyond simple image-caption pairs to enhance generalization and alignment. Our method addresses the stated limitations by introducing bidirectional attention through continual pre-training, scaling effectively with massive unlabeled datasets via joint reconstruction objectives, and utilizing diverse multimodal data for enhanced representation robustness. Experiments demonstrate that MoCa consistently improves performance across MMEB and ViDoRe-v2 benchmarks, achieving new state-of-the-arts, and exhibits strong scalability with both model size and training data on MMEB.We have released the model weights and data on our project page https://haon-chen.github.io/MoCa/.