Hello @Annetta .
Based on the answers you have provided about the situation, my conclusions are
(a) Assuming that your husband's income is all associated with the school i.e. scholarship and stipends etc. and covered by 1098-T from the school, you can file as Married Filing Joint but keep your foreign income outside US purview because your residency start date is Sept. 21.2019.
(b) The cleanest filing would be for your husband to file a Dual Status. This would mean filing form 1040-NR or 1040-NR/EZ ( as he has done for the past few years -- and not supported by TurboTax, but his school or SprinTax can help ) covering. Then preparing a form 1040 ( supported by TurboTax ) as Married Filing Joint, covering the rest of the year. Note that this could mean filing by mail but it may be a better ( besides being conservatively correct ) taxwise. It also excludes your foreign income since your residency started on Sep. 21 2019.
(c) For California purposes, there is two approach again ---- 1. you file a joint return where your husband is a resident for the year and the wife's residency start date is Sept. 21 2019 -- thus excluding your prior foreign income.; 2. your husband files a resident return ( married filing Sep ) and you do not file anything. Method one is the most conservative and meets the intent of the law. Also note that whichever you file, the federal and state should be in tune -- since California ( like most states ) depend on the federal return for congruence.
Hope this helps. If you have more , especially since your scenario is becoming specific to you and probably not helpful to others, you can PM me
