Gene co-expression networks capture biologically important patterns in gene expression data, enabling functional analyses of genes, discovery of biomarkers, and interpretation of genetic variants. Most network analyses to date have been limited to assessing correlation between total gene expression levels in a single tissue or small sets of tissues. Here, we built networks that additionally capture the regulation of relative isoform abundance and splicing, along with tissue-specific connections unique to each of a diverse set of tissues. We used the Genotype-Tissue Expression (GTEx) project v6 RNA sequencing data across 50 tissues and 449 individuals. First, we developed a framework called Transcriptome-Wide Networks (TWNs) for combining total expression and relative isoform levels into a single sparse network, capturing the interplay between the regulation of splicing and transcription. We built TWNs for 16 tissues and found that hubs in these networks were strongly enriched for splicing and RNA binding genes, demonstrating their utility in unraveling regulation of splicing in the human transcriptome. Next, we used a Bayesian biclustering model that identifies network edges unique to a single tissue to reconstruct Tissue-Specific Networks (TSNs) for 26 distinct tissues and 10 groups of related tissues. Finally, we found genetic variants associated with pairs of adjacent nodes in our networks, supporting the estimated network structures and identifying 20 genetic variants with distant regulatory impact on transcription and splicing. Our networks provide an improved understanding of the complex relationships of the human transcriptome across tissues.