If I face a new patient with atopic dermatitis (AD) and co-morbid asthma (BA), I would first consider the age, status of IgE, status of allergic sensitivity (meaning allergy work up with skin test or RAST) before I consider the treatment. Why the age is important? I refer you to look at Fig.7.11 (in Allergy, 2nd edition, ed by Holgate & others, 2001, Mosby) in which the incidence of four major allergic manifestations and age was illustrated. For instance, food allergy is an important underlying cause of AD in younger age. Therefore, food allergy work up for AD should be attempted. Incidence of asthma arises from age 6, reaches the peak at 10. In this age group, work up of environmental factors is useful. All those efforts are aimed to find the possible causes. The removal of the cause should be in the scheme of the treatment of AD and asthma. As for medical management of AD, other than removing offending factors, make sure there is no superficial infection. Use of topical anti-inflammatory factors and skin care should be emphasized. There are many-anti-inflammatory agents (corticosteroid inhaler) available for the management of asthma. If the management is ineffective, we could start consider deciding the phenotypes of asthma. At that stage, use of biological agents, such as monoclonal antibody to IgE, or IL-5 for eosinophils, or combo of IL-4 and13 could be considered. Pending on the progress, we could take a step wise approaches.
In addition to Shih-Wen's answer, it would appear that topical therapy for both (usually steroid based) would be the recommended strategy, beyond avoidance of potential triggers. The monoclonal antibodies are recommended as add-on therapies for asthma (in addition to ICS/LABA and possibly Tiotropium). Oral corticosteroid therapies though effective are limited by side-effects.
If a patient is above the age of six, I would regularly make sure AD is not affected by superficial infection. A course of six days of PO antibiotics would help decrease bacterial load, especially when the skin lesions looked wet and bloody. Since we know most superficial infection was brought by inadvertent scratches of the lesions by patients, I would spend time teaching patients a "biofeedback control" to avoid scratching. It may take some practices to make it work, the results of this holistic approach have been very rewarding. It helps diminishes the dependence of the use of medication, especially the corticosteroid.