Acoustic modeling serves audio processing tasks such as de-noising, data reconstruction, model-based testing and classification. Previous work dealt with signal parameterization of wave envelopes either by multiple Gaussian distributions or a single asymmetric Gaussian curve, which both fall short in representing super-imposed echoes sufficiently well. This study presents a three-stage Multimodal Exponentially Modified Gaussian (MEMG) model with an optional oscillating term that regards captured echoes as a superposition of univariate probability distributions in the temporal domain. With this, synthetic ultrasound signals suffering from artifacts can be fully recovered, which is backed by quantitative assessment. Real data experimentation is carried out to demonstrate the classification capability of the acquired features with object reflections being detected at different points in time. The code is available at https://github.com/hahnec/multimodal_emg.