Nature Communications has had a policy since 2016 that authors are given the option to publish the peer review history of their paper.
Are there other journals with the same initiative?
The publisher Cooernicus has an open peer-review process, i.e. all peer-reviewer reports as well as the answers of the author(s) are published open access.
The peer reviews for several highly regarded machine learning conferences (most notably the ICLR - International Conference on Learning Representations) can be found at https://openreview.net/. While these are not 'journals' in the strictest sense, they do have a peer-review process. The setup is however double-blind.
The website, e.g. for the ICLR allows you to do the following: