Mendelian randomization (MR) provides valuable assessments of the causal effect of exposure on outcome, yet the application of conventional MR methods for mapping risk genes encounters new challenges. One of the issues is the limited availability of expression quantitative trait loci (eQTLs) as instrumental variables (IVs), hampering the estimation of sparse causal effects. Additionally, the often context- or tissue-specific eQTL effects challenge the MR assumption of consistent IV effects across eQTL and GWAS data. To address these challenges, we propose a multi-context multivariable integrative MR framework, mintMR, for mapping expression and molecular traits as joint exposures. It models the effects of molecular exposures across multiple tissues in each gene region, while simultaneously estimating across multiple gene regions. It uses eQTLs with consistent effects across more than one tissue type as IVs, improving IV consistency. A major innovation of mintMR involves employing multi-view learning methods to collectively model latent indicators of disease relevance across multiple tissues, molecular traits, and gene regions. The multi-view learning captures the major patterns of disease relevance and uses these patterns to update the estimated tissue relevance probabilities. The proposed mintMR iterates between performing a multi-tissue MR for each gene region and joint learning the disease-relevant tissue probabilities across gene regions, improving the estimation of sparse effects across genes. We apply mintMR to evaluate the causal effects of gene expression and DNA methylation for 35 complex traits using multi-tissue QTLs as IVs. The proposed mintMR controls genome-wide inflation and offers insights into disease mechanisms.