Unfortunatly Arocobalena does not explain, which day day pass?
To take your bike with you on routes offering bike transport, a ticket must be purchased at the reduced price for the route required. If the price is higher than CHF 14, a Day Pass Bike has to be bought at the reduced price. For information on transporting bicycles, please contact the relevant transport companies.
I would say SBB Day Pass Bike is valid on Tilo trains to Chiasso, but it is not possible to buy day pass bike together with a ticket from Lugano - Monza - Milano.
Good news, bike gratis Chiasso to Milano 😉 , since 1st of april 2024?
https://www.lombardianotizie.online/bici-gratis-treni/
Please check information together with Kontaktaktcenter, if information is true your sbb bike pass is valid to Chiasso and witout a ticket for free Chiasso to Milano. Please check timetable for restrictions fir bycicles.
Kind regards
Christoph