Can my husband travel to China with me using his Chilean passport?

As long as China will issue a visa on his Chilean passport (and they might have questions about his status in the US and why he's not using his US passport if he is applying at a Chinese consulate in the US), he should have no problem traveling leaving the US and entering China, as well as exiting China, on his Chilean passport (once China's COVID-19 entry restrictions for foreigners are lifted).

As for entering the US (or more importantly, getting the airline to let him board a flight to the US), he will likely need a US passport. Although as a US citizen with proof of US citizenship, he cannot be denied entry to the US if he makes it to a port of entry, airlines are not supposed to let him board without one of the allowed documents. As a US citizen, he is not eligible for a US visa, and may have trouble getting an ESTA on his Chilean passport (although some US dual nationals have reported success).

Although he cannot be issued a regular US passport due to back child support, he can still be issued a limited US passport that is valid for direct return to the US. See archived 7 FAM 1387.2(e):

Issuance of Limited Passport for Direct Return to United States: Passport services for individuals with P/H Lookouts who are overseas are restricted to issuance of a passport limited to the time required for travel to the United States, generally just a few days and no longer than two weeks. The applicant is charged a fee for this passport, unless one of the exemptions provided in 7 FAM 1350 Appendix G applies. Endorsement code 105 must be used for all child support arrearage cases. (See 7 FAM 1300 Appendix B, Endorsement Codes.)

(SBU) Endorsement 105

“THIS PASSPORT IS VALID ONLY FOR RETURN TO THE UNITED STATES BEFORE (month day, year). IT CANNOT BE EXTENDED.”

and archived 7 FAM 1365 for more information on emergency passports.

So it seems he could go to a US consulate in China right before his intended return to get a very short duration limited US passport for return to the US.

If he can't get a US passport, and he can make it to Canada or Mexico (which Chilean citizens can normally visit without a visa, though COVID-19 might make this more difficult), another option is for him to go to Canada or Mexico first and then cross the land border into the US with proof of his US citizenship, and not worry about airlines not letting him board.