I'm no linguist or SLP, but it's not so much a matter of Chinese language
acquisition in a baby than how much exposure your baby is getting to a particular language on a consistent basis.
Read "What's Going On In there: How the brain and mind develop in the first five years of life" by Lise Eliot if you want the long answer to this question.
All babies' brains are wired from birth to be receptive to human communication in any and every language. With repeated exposure to certain tones and sounds pertaining to the language(s) s/he hears from birth to age 2-3 yrs (check the book for the exact age) the neurons begin to pare down the neuropathways that would have been receptive to sounds belonging to languages s/he doesn't get a chance to hear.
For the record, I am a somewhat native speaker of Cantonese, and a SAHM to our 3 kiddies. The eldest spoke mostly Chinese at the beginning, but that fluency is now eclipsed by French, as DH and my in-laws are here in the city, whereas my family lives a good 600 km away.
DD hears French and English from her older brother, who now goes to school in English and French, so her Chinese isn't as strong as her brother's was at that age.
DS2 understands me quite well, but at 13 months his babbling is anybody's guess whether it's Chinese or French. He signs a little though
Both DS1 and DD were capable of code switching (speaks to Mom in Chinese and Dad in French) from the time they were about 18 months onwards.
If your child is otherwise healthy and hitting all other developmental milestones on time, do not worry. If s/he has other health issues which lead you to suspect otherwise, listen to your instincts.
A child in a unilingual or
multi-lingual milieu can have speech/language problems, but that shouldn't discourage you both from communicating with your child in your respective native tongues. If anything, having a solid grounding with both of you modelling correct language and speech patterns in Italian and Mandarin will help your child to spit things out correctly--as soon as the brain figures out a way to digest and process both more efficiently!