An absorbent article (10) which includes a backsheet layer (30) having a pair of laterally opposed and longitudinally extending side margins (20). Each side margin has an outwardly concave, terminal side edge contour (15) located at appointed leg opening regions (17) in an intermediate portion (16) of the side margin. Each concave side edge contour (15) has a selected longitudinal extent along a length dimension (26) of the article (10). A liquid permeable topsheet layer (28) is connected in a superposed facing relation to the backsheet layer (30), and an absorbent body (32) is sandwiched between the topsheet layer (28) and the backsheet layer (30). A separately provided gusset-flap composite member (19) is connected to at least one of the backsheet and topsheet layers along each of the leg opening regions (17). The gusset-flap member (19) provides a leg gusset section (142) and a containment flap section (144), and is distinctively configured to provide improved leakage resistance, fit and comfort.