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Modeling complex geological interfaces is a common task in geosciences. Many data sources are available for geological interface modeling, including borehole data and geophysical surveys. Geological knowledge, such as the delineation from geologists, is difficult to quantify but likely adds value to geological interface modeling. To integrate all information, we present a data-knowledge-driven trend surface analysis method to construct stochastic geological interfaces. We design a Metropolis–Hastings sampling framework to sample stochastic trend interfaces and quantify the uncertainty of geological interfaces given all information sources. This method is suitable for both explicit and implicit representations of geological interfaces. We demonstrate our method in three different test cases: modeling stochastic interfaces of Greenland subglacial topography, magmatic intrusion, and buried river valleys in Australia. • This new trend surface analysis method integrates various data types and geological knowledge. • A Markov chain Monte Carlo sampler is used for explicit and implicit geological interfaces. • Stochastic geological interfaces are sampled in three studies: subglacial topography, magmatic intrusion, and palaeovalley modeling. [ABSTRACT FROM AUTHOR]