Mobile and wearable devices are being increasingly used for developing audio based machine learning models to infer pulmonary health, exacerbation and activity. A major challenge to widespread usage and deployment of such pulmonary health monitoring audio models is to maintain accuracy and robustness across a variety of commodity devices, due to the effect of device heterogeneity. Because of this phenomenon, pulmonary audio models developed with data from one type of device perform poorly when deployed on another type of device. In this work, we propose a framework incorporating feature normalization across individual frequency bins and combining task specific deep neural networks for model invariance across devices for pulmonary event detection. Our empirical and extensive experiments with data from 131 real pulmonary patients and healthy controls show that our framework can recover up to 163.6% of the accuracy lost due to device heterogeneity for four different pulmonary classification tasks across two broad classification scenarios with two common mobile and wearable devices: smartphone and smartwatch.Clinical relevance- The methods presented in this paper will enable efficient and easy portability of clinician recommended pulmonary audio event detection and analytic models across various mobile and wearable devices used by a patient.