Incomplete scenario is a prevalent, practical, yet challenging setting in Multimodal Recommendations (MMRec), where some item modalities are missing due to various factors. Recently, a few efforts have sought to improve the recommendation accuracy by exploring generic structures from incomplete data. However, two significant gaps persist: 1) the difficulty in accurately generating missing data due to the limited ability to capture modality distributions; and 2) the critical but overlooked visibility bias, where items with missing modalities are more likely to be disregarded due to the prioritization of items' multimodal data over user preference alignment. This bias raises serious concerns about the fair treatment of items. To bridge these two gaps, we propose a novel Modality-Diffused Counterfactual (MoDiCF) framework for incomplete multimodal recommendations. MoDiCF features two key modules: a novel modality-diffused data completion module and a new counterfactual multimodal recommendation module. The former, equipped with a particularly designed multimodal generative framework, accurately generates and iteratively refines missing data from learned modality-specific distribution spaces. The latter, grounded in the causal perspective, effectively mitigates the negative causal effects of visibility bias and thus assures fairness in recommendations. Both modules work collaboratively to address the two aforementioned significant gaps for generating more accurate and fair results. Extensive experiments on three real-world datasets demonstrate the superior performance of MoDiCF in terms of both recommendation accuracy and fairness. The code and processed datasets are released at https://github.com/JinLi-i/MoDiCF.