To use the 1/4" headphone portion of the BPHS1 with a 3.5mm (1/8th inch) connection, one would need a step-down (1/4" to 1/8") headphone adapter, such as the Hosa MHE100.5. You can always contact an Authorized ATUS (Audio-Technica United States) Dealer to ask about a headphone step-down adapter. There is an Authorized ATUS Dealer List and Locator on www.audio-technica.com
However, you might want to look into sending the headphone output of your computer into your mixer. This way, you would likely not need an adapter for a BPHS1.
If you have any further questions, or for any further correspondence, please contact the ATUS (Audio-Technica United States) Audio Solutions Team at firstname.lastname@example.org, and include both your original question and this response.