Aims. We study the sub-AU-scale circumstellar environment of the Herbig Ae star HD 144432 with near-infrared VLTI/AMBER observations to investigate the structure of its inner dust disk. Methods. The interferometric observations were carried out with the AMBER instrument in the H and K band. We interpret the measured H- and K-band visibilities, the near- and mid-infrared visibilities from the literature, and the spectral energy distribution (SED) of HD 144432 by using geometric ring models and ring-shaped temperature-gradient disk models with power-law temperature distributions. Results. We derive a K-band ring-fit radius of 0.17 ± 0.01   AU and an H-band radius of 0.18 ± 0.01   AU (for a distance of 145   pc). This measured K-band radius of  ~0.17   AU lies in the range between the dust sublimation radius of  ~0.13   AU (predicted for a dust sublimation temperature of 1500   K and gray dust) and the prediction of models including backwarming (~0.27 AU). We find that an additional extended halo component is required in both the geometric and temperature-gradient modeling. In the best-fit temperature-gradient model, the disk consists of two components. The inner part of the disk is a thin ring with an inner radius of  ~0.21   AU, a temperature of  ~1600   K, and a ring thickness  ~0.02   AU. The outer part extends from  ~1   AU to  ~10   AU with an inner temperature of  ~400   K. We find that the disk is nearly face-on with an inclination angle of  <\hbox{$28\degree$}28◦. Conclusions. Our temperature-gradient modeling suggests that the near-infrared excess is dominated by emission from a narrow, bright rim located at the dust sublimation radius, while an extended halo component contributes  ~6% to the total flux at 2   μm. The mid-infrared model emission has a two-component structure with  ~20% of the flux originating from the inner ring and the rest from the outer parts. This two-component structure is indicative of a disk gap, which is possibly caused by the shadow of a puffed-up inner rim.