Spectrum maps reflect the utilization and distribution of spectrum resources in the electromagnetic environment, serving as an effective approach to support spectrum management. However, the construction of spectrum maps in urban environments is challenging because of high-density connection and complex terrain. Moreover, the existing spectrum map construction methods are typically applied to a fixed frequency, which cannot cover the entire frequency band. To address the aforementioned challenges, a UNet-based data-and-semantic dual-driven method is proposed by introducing the semantic knowledge of binary city maps and binary sampling location maps to enhance the accuracy of spectrum map construction in complex urban environments with dense communications. Moreover, a joint frequency-space reasoning model is exploited to capture the correlation of spectrum data in terms of space and frequency, enabling the realization of complete spectrum map construction without sampling all frequencies of spectrum data. The simulation results demonstrate that the proposed method can infer the spectrum utilization status of missing frequencies and improve the completeness of the spectrum map construction. Furthermore, the accuracy of spectrum map construction achieved by the proposed data-and-semantic dual-driven method outperforms the benchmark schemes, especially in scenarios with low sampling density.