What do you mean by a "splitter cable"? Is this a cable designed for plugging two headphones into a single headphone socket? If so, you are connecting the left input of the H2 to the left output of the stereo microphone, but the right input of the H2 is connected to both the right output of the stereo microphone and also the output of the mono microphone.

Since the microphones draw their operating power from the input connector (they use "plug-in power"), it's not going to give good results on the right channel that is both powering and receiving signals from two microphones. The mono microphone has no connection to the tip contact of its jack plug.

One thing you could try is to disconnect the ring connection on one of the output sockets on your splitter cable, and label that socket carefully so you only plug the stereo microphone into it. Leave the tip and sleeve connections as they are. Doing that would allow the right channel of the H2 to power and receive signal only from the mono microphone plugged into the other (unmodified) socket. You would have to use the stereo microphone as mono, with the left side of the microphone pointed towards the sound source.

Good luck!

Yes, it is a headphone splitter cable. I peeled some of the PVC sleeving off one branch of the Y - and then found that the battery on my continuity meter is flat! I look forward to getting a replacement and finding out which wire to cut.
Thanks very much for your help.