Family Law Questions? Ask a Family Lawyer Online.
Yes, the judge can order that. This is a temporary order, and generally whoever has temporary custody of the child will also get custody of the home until a permanent order can be issued (after a more thorough hearing).
As for their joint assets, they both still own them. Usually in the temporary order the judge issues something saying that neither party is to dispose of any assets, or incur debts. The personal property will be divided at a later date.