The taxpayer has the option to file a Joint tax return with his spouse.  If they do that, both of their worldwide incomes will be entered on the tax return.  If the spouse is a Nonresident Alien, they would need to make the election to treat the spouse as a Resident.

https://www.irs.gov/publications/p519#en_US_2018_publink1000222196

Yes, if they file a Joint tax return, they can probably claim their children (assuming they meet the regular requirements of being a dependent) which could possibly result in some tax benefits. [Edited]

Sorry, I need to correct part of my prior answer.  The dependents would NOT qualify for the $500 credit unless they are a Resident of the US.  However, there could be other benefits (medical expenses, Premium Tax Credit household size, State exemptions, etc.).