A sound absorptive multilayer composite having an air-impermeable barrier, an air-permeable reinforcing core having an airflow resistance of at least about 100 mks Rayls and a thickness at least about 1/3 the final composite thickness, an air-permeable open cell foam or fibrous pad having an airflow resistance less than about 2000 mks Rayls and a thickness at least about 1/10 the final composite thickness and a semipermeable airflow-resistive membrane having an airflow resistance of about 500 to about 4000 mks Rayls can provide improved acoustic performance. For example, existing vehicular headliner designs may be improved by adding a properly chosen and properly positioned semipermeable airflow-resistive membrane, a properly chosen and properly positioned air-impermeable barrier, or a properly chosen and properly positioned open cell foam layer.