For witch organisms? Unfortunately, we don't have too much data integration yet even for model organisms, in the ENCODE database ( https://www.encodeproject.org/ ) you find some proteomics data together with expression, but really for few samples, and in general you will find such datasets spread over different databases/papers (so, organism/experiment specific cases), even if this discussion was already raised since many years ago https://genome.cshlp.org/content/27/1/133.full.html ). Maybe some other colleague is aware of some database already done, but so far I never came across any good one.
As Rafael said, it is tough to find an integrated database, and I also don`t know any. However, I have some papers with me on the subject. One is a review on the topic of transcriptomic and proteomic data integration that might have something to could aid you in this matter - this paper provides an extremely comprehensive review, with a lot of focus on bioinformatics. Here [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3637682/] .
The other is a study published in Sci. Rep. that uses three types of data (genomics, transcriptomics, and proteomics), which they provide the link to download their results. It might be useful to you, in some way. Here [https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4700448/].
You might find this paper interesting: Article A deep proteome and transcriptome abundance atlas of 29 heal...
They perform proteomic and transcriptomic analysis of paired samples from 29 human tissues. The raw data is available via links in the 'Data availability' section.