No, if the K-1 is in his name and he is reporting it on his return, then you do not include the K-1 on your return when filing separate, unless you are in a community property state.
Updating this for California being a community property state, as since your spouse is a resident of CA and the income is his, then it would be deemed community income and need to be split:
Division of Income:
California is a community property state. The domicile
of the spouse/RDP earning the income determines
the division of income between spouses/RDPs when
separate returns are filed. Each spouse/RDP must follow
the laws in his or her state of domicile to determine
whether income is separate or community. When
separate returns are filed, you and your spouse/RDP
must each report half of the community income plus all
of your separate income on your return.
https://www.ftb.ca.gov/forms/2018/18_1031.pdf
[Edited 3-14-19|11:04am]
