They can break the server SSL connection at the proxy and instantiate a new new one from the proxy to your pc. Since they control DNS and the HTTP stream, they can ostensibly claim that the proxy is the server you are connecting to.
They can only do this if they control the client PC as well as the proxy, as they would need to install the relevant root CA cert in your browser, otherwise it will complain, since they are using self-signed certs for this.
I would consider it unsafe to conduct anything you need to remain private.
I would not be doing anything which required security on one of those machines.