Your daughter’s chances of catching the bronchitis from your husband depends on two main factors:
Firstly, there are numerous antibiotics for pediatric patients and the type and dosage are required to determine if there is cross coverage. It is unclear from your question which antibiotic and what dosage your daughter is on.
Secondly, and more importantly, over 90% of adult bronchitis are caused by viral organisms (the vast majority by adenovirus) for which no antibiotic can prevent or treat. The bacterial causes of bronchitis are usually found in chronic smokers. Streptococcus pneumonia is the most common offending organism and is covered by most antibiotics such as azithromycin (Z-pack).
Chances are your husband’s bronchitis is viral in origin and your daughter’s antibiotics offer no protection. Therefore, proper hand washing, and avoiding close contact with those indviduals with bronchitis are the most important steps your daughter can take.