You'd need to use an ADAT-to-SPDIF (or AES) adapter box like RME's ADI4-DD or similar.
http://www.rme-audio.de/en/products/adi_4_dd.php
The Alphalink can handle the MADI-to-ADAT portion of the conversion (assuming you aren't using the Alphalink AX's additional ADAT Outputs for a different use) - so you can skip an expensive MADI-to-SPDIF (or AES) converter.
A different solution might be to consider the RME MADI-FX card that has a dedicated AES I/O, and adds TM-FX. Personally, I splurged for the MADIface-XT model, and am very glad to have TM-FX above the old MADI HDSPe card it replaced. Then, my "old" MADI HDSPe card was handed-down to a slave DAW, and now has 128 I/O's to the main DAW over MADI!
The MADIface-XT also works with RME's ARC monitor controller - the MADI-FX does not (nor does your current MADI HDSPe). The ARC has become a critical part of my mixer-less workflow, and would not want to imagine working without it.
All food for thought for long-term investments IMO
MADIface-XT+ARC / 3x HDSP MADI / ADI648
2x SSL Alphalink MADI AX
2x Multiface / 2x Digiface /2x ADI8