The exchange of gases, oxygen for carbon dioxide, takes place between the alveoli and the pulmonary capillaries. This is known as the pulmonary exchange, and is part of the overall process of respiration, or breathing as we usually call it. So these capillaries are woven into the tissue of the alveoli, and the exchange takes place in the connective tissue between them. It also helps to think of capillaries - any capillary - as a method of delivering blood to the tissues (as opposed to other major organs), and the alveoli as the means for delivering gases, both the inhalation of oxygen and transfer to the bloodstream, then the removal of carbon dioxide from the blood followed by exhalation. I hope that helps.