Yes. You can access HTTPS services via the HTTP proxy whilst still getting full SSL/TLS security.
When you make a request via the proxy to an HTTPS endpoint your client should transparently issue a CONNECT request rather than a basic GET request.
On receipt of this CONNECT request the proxy will open a tunnel between your client and the endpoint, allowing your client to negotiate a standard SSL session with the endpoint.
Once negotiated all traffic sent between your client and the endpoint will be encrypted as if you had connected directly with them.
We are also testing HTTPS proxy endpoints, please contact us if you want to trial it.
With HTTPS endpoint your initial CONNECT request will be also encrypted, this protects proxy credentials and remote hostname but will require additional TLS handshake.
Please note that HTTPS endpoints are only supported by libcurl based HTTP client libraries, we recommend to check if your language has bindings for it.