In recent years extensive studies on the Earth's climate system have been carried out by means of advanced complex network statistics. The great majority of these studies, however, have been focusing on investigating correlation structures within single climatological fields directly on or parallel to the Earth's surface. In this work, we develop a novel approach of node weighted interacting network measures to study ocean-atmosphere coupling in the Northern Hemisphere and construct 18 coupled climate networks, each consisting of two subnetworks. In all cases, one subnetwork represents monthly sea-surface temperature (SST) anomalies while the other is based on the monthly geopotential height (HGT) of isobaric surfaces at different pressure levels covering the troposphere as well as the lower stratosphere. The weighted cross-degree density proves to be consistent with the leading coupled pattern obtained from maximum covariance analysis, while network measures of higher order allow for a further analysis of the correlation structure between the two fields. Zonally averaged local network measures reveal the sets of latitudinal bands for which there exists a strong correlation between parts of the ocean and the atmosphere. Global network measures quantify the strength of these similarities and identify atmospheric layers which form dynamical clusters of comparable strength with the ocean. All measures consistently indicate that the ocean-atmosphere coupling in the Northern Hemisphere follows a hierarchical structure in the sense that large areas in the ocean correlate with multiple dynamically dissimilar areas in the atmosphere.