Are Unit Members children able to attend BUSD?

Yes

BCCE contract

6.12 Enrollment at Berkeley Schools

The children of unit members who do not reside in Berkeley shall be admitted to Berkeley schools,

 subject to the granting of a permit by the district of residence.

Further, should a unit member request that his/her child be permitted to enroll at the school to which s/he is assigned,

the District will make every effort to enroll the child at the site in the Spring when students are normally assigned.