Accurate estimation of acoustic impedance from seismic data is crucial for extracting petrophysical parameters, such as porosity and lithology, to enhance reservoir characterization. However, the band-limited nature of seismic data leads to an imperfect estimation of acoustic impedance. The missing low-frequency portion of the band-limited data is essential for recovering accurate, absolute impedance values. However, limitations in seismic acquisition make it difficult to obtain data at the low-frequency end, specifically below 5Hz. Recently, deep learning (DL) algorithms have demonstrated significant potential in retrieving missing low-frequency information. However, DL algorithms often require a substantial amount of labeled data (e.g., impedance logs), which are generally either very scarce or unavailable for sufficient training in real field applications. To address this challenge, we present an innovative adaptive domain adversarial neural network (aDANN) for broadband acoustic impedance inversion from real seismic data. Unlike conventional transfer learning approaches, aDANN does not require two subsequent phases of pre-training and adaptation. Instead, it jointly trains the source domain (with sufficient labels) and the target domain (with few or no labels) in an adversarial manner, aiming to promote the emergence of domain-invariant deep features. Furthermore, seismic envelope and instantaneous phase attributes are used as auxiliary inputs in the aDANN model to compensate for the missing low-frequency information in post-stack seismic data. The effectiveness of the designed framework is tested on a synthetic SEAM subsalt model and field data from the F3 block in the North Sea. Further, comparisons with other standard methods show that the proposed approach outperforms them in terms of accuracy, robustness, and computational cost. Thus, the study provides a superior workflow for absolute impedance inversion from field data, and the outcome will facilitate an improved interpretability of seismic data in both quantitative and qualitative aspects, thereby improving reservoir characterization.