According to the page that you referenced for the mic, it states that:
Please note that all versions of the Sennheiser ME3 (sold here or elsewhere) are wired differently than usual headset microphones and are not electrically compatible with many computer sound cards
This explains the issue that you are experiencing.
Further, they go on to say:
This microphone is completely functional, however, when used in conjunction with an Andrea USB sound adapter, the Buddy 6G or 7G USB adapter, and the Andrea Pure Audio USB Adapter. We recommend purchasing our "ME3 combo" (pictured above) for predictably great results.
I suggest getting the Andrea Pure Audio USB Adapter
Is there a reason you need this splitter for a microphone? I didn't get that from your description of the problem.
EDIT:
I noticed in one of the comments you said you didn't want to use up one of the USB ports. Have a look at these USB Hubs by Anker. I personally use these and I can attest to their customer service - their return and support policy is beyond fantastic.