  Change detection plays a fundamental role in Earth observation for analyzing
temporal iterations over time. However, recent studies have largely neglected
the utilization of multimodal data that presents significant practical and
technical advantages compared to single-modal approaches. This research focuses
on leveraging {pre-event} digital surface model (DSM) data and {post-event}
digital aerial images captured at different times for detecting change beyond
2D. We observe that the current change detection methods struggle with the
multitask conflicts between semantic and height change detection tasks. To
address this challenge, we propose an efficient Transformer-based network that
learns shared representation between cross-dimensional inputs through
cross-attention. {It adopts a consistency constraint to establish the
multimodal relationship. Initially, pseudo-changes are derived by employing
height change thresholding. Subsequently, the $L2$ distance between semantic
and pseudo-changes within their overlapping regions is minimized. This
explicitly endows the height change detection (regression task) and semantic
change detection (classification task) with representation consistency.} A
DSM-to-image multimodal dataset encompassing three cities in the Netherlands
was constructed. It lays a new foundation for beyond-2D change detection from
cross-dimensional inputs. Compared to five state-of-the-art change detection
methods, our model demonstrates consistent multitask superiority in terms of
semantic and height change detection. Furthermore, the consistency strategy can
be seamlessly adapted to the other methods, yielding promising improvements.
