Medium Large Transport
Flight Crew Air Transport Pilot (ATP)
Communication Breakdown; Training / Qualification
Conflict Airborne Conflict; Deviation - Speed All Types; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter Weather / Turbulence
Flight Crew Executed Go Around / Missed Approach
Human Factors; Weather
The weather was 900 overcast and 10 miles visibility.  We were cleared by Center for the ILS a transition. The First Officer (FO) Pilot Monitoring (PM) was making the appropriate radio calls on CTAF and the approach was proceeding normally until we were on about a 3 mile final when we heard a radio call from another aircraft saying that he was departing the opposite direction runway.  My FO immediately told him that we were on the ILS for inside of a 3 mile final to which the other pilot replied something to the effect of 'I'm already throttled up and departing!'. Since we were just entering the tops of the clouds and the VFR plane would soon be entering the bases of the clouds head on to us I decided to execute a missed approach. During the missed approach the flaps (15 degrees) were overspend by approximately 20 knots. We were cleared for a second approach from ATC which was executed uneventfully. The other pilot had obviously not been monitoring CTAF while taxiing out as we made several position reports while on the approach and the first call he made was that he was rolling down the runway coming right at us.
Two aircraft in a CTAF environment conflicted during an approach and departure in IMC conditions.