Yes. L-2 spouses are employment-authorized incident to status. Children in dependent status may generally study but are not authorized to work.
Spouse employment is a status consequence
This is one of the clearer advantages of the L route for a household, and it changes the arithmetic of a move that a single-income category would not support. The spouse's work permission follows from the status itself rather than from any employer's sponsorship, and the practical questions are documentary: what evidence of status an employer will accept, and how that evidence is renewed alongside the principal's status.
Children accompanying the family may generally attend school under the published guidance on study, but dependent status carries no work permission for them at any age. A child who wants to work while at university would need their own basis, and a child approaching adulthood needs their own status planning well before the dependent classification stops fitting.