Dementia is a major and growing global health burden, with Alzheimer's disease (AD) accounting for most cases. Timely and accurate diagnosis is central to managing this burden and increasingly depends on integrating complementary clinical and imaging information. Multimodal deep learning can combine these modalities for AD diagnosis, but how its explanations behave across modalities, fusion strategies, and cohorts remains unclear. We developed an explainable multimodal framework pairing a 3D CNN encoder for T1-weighted MRI with a feedforward network for harmonized clinical and demographic data, comparing varied model setups on three-way and pairwise diagnostic tasks using 6,479 internal records from the ADNI and 1,703 independent records from the OASIS-3. On ADNI, the tabular-only model achieved the highest three-class AUC-ROC of 0.879 and best discriminated cognitively normal (CN) versus mild cognitive impairment (MCI; 0.903), while cross-attention performed best for MCI versus AD (0.861); CN versus AD was highly discriminative overall. On OASIS-3, the vision-only model performed best (three-class AUC-ROC 0.910); CN versus MCI remained difficult, and no fusion strategy consistently outperformed single modalities across tasks and cohorts. SHAP and Integrated Gradients identified the MMSE as the dominant tabular feature in both cohorts, with global feature rankings agreeing strongly in ADNI (
ρ=0.94) and OASIS-3 (
ρ=0.96); CAM-based explanations, however, changed with model configuration and cohort. These findings show that multimodal performance and explanations are task, modality, fusion, and cohort-dependent: a dominant cognitive signal persisted across cohorts, but feature contributions and CAM explanations did not, underscoring the need to evaluate explainability under cohort shift rather than as a stable, intrinsic property.