A helicopter cleared for an ILS approach suffers repeated failures to capture the LOC and GS followed by the autopilot disconnecting. An unintended climb of 600 feet occurs.

Narrative

We were cleared to 2000 feet established inbound to MOREE beacon on the 227 course on the ILS 23 at MMU. After the aircraft was established inbound to MOREE we armed the approach for the ILS. The ILS was on the appropriate frequency 110.30. The LOC captured and switched over from the FMS and showed green needles with an invalid G/S signal. Within 1-2 seconds we lost the LOC signal and the AP disconnected and slowly pitched up with no decouple voice warning. We reengaged the LOC and it repeated the sequence of capture then loss of signal G/S first then LOC. On the third engagement at at 2nm from MOREE it captured both the LOC and G/S. At this point we were approximately 2600 feet descending on the G/S and Established on the LOC. At approximately 1nm from MOREE tower called and said approach called and asked why we climbed. I reported that we had lost the LOC and G/S signals and were reestablished and correcting. Tower also reported at this time that they had a thunderstorm over the field with approximately 3/4 mile visibility in heavy rain. We witnessed a lighting strike @ 5nm away to the east. With the loss of signal and de-coupling of the ILS we should have hand flown the aircraft and maintained our altitude instead of trouble shooting the AP ILS couple issue with loss of signal. An alternative would have been to execute an immediate missed approach an inform ATC of the problem.