I think the only way is to do a local copy on the machine where you are sit, then transfer files on the other server. I really don't know if you can copy on the fly, unless you have access to one of the two servers.
To recursively copy folders, it depends on the transfer protocol you're allowed on these machines. If using Secure Shell you can simply do
scp -r user@host:/path/to/directory/to/copy /path/to/local/directory
If using ftp you can try wget like this
wget -r -nH --ftp-user=username --ftp-password=password ftp://host/path/to/dir/*