Hi lonka, I do not have a baby that is white chinese mix. But I do have cousins who are inter - racially mixed.
From what I know so long as you bring your child, your original marraige certificate, your original foreign registered birth certificate, original travel documents to ICA. Your should be able to register for a sg bc .
As for registering with Chinese writings in the bc.So long as one of the parents are Chinese it can be included in the bc.
The Chinese surname does not have to follow your surname. Or your hubby's surname translated in chinese.
Your can have something meaningful and inspiring, so long as the name does not have an offending meaning to others. But most people will use their mom' actual chinese surname to give the child a actual "identity link" to the child's partial chinese roots.
You can double-check on ica's official website: www.ica.gov.sg for more details. ☺