The procedure for getting out of rain ice is the subject of some argument. We teach climb as a first option, descend (if you have air traffic and obstacle clearance) as a second option and turnback as the least suitable.
There are sound thermodynamic reasons for climbing into the warm rain - you get a quicker clearance of ice from the airframe. The source we use is the Handbook of Aviation Meteorology - check pages 138 and 136
One feedback question we heard of gave "climb until clear of cloud" as an option, which is nonsense, as the cloud at a warm front goes up to FL300 and above. In that question they told you in the preamble that it was ok to descend, so the No 2 option became the No 1
I do not agree with Wickson, but hey, live like you wanna live, it's a free country
Dick W