Effectively mobilizing displacement and predicting mobilization pressure in a porous-type reservoir filled with bubbles or blobs require the knowledge of variation of contact angles and capillary pressure. A bubble/blob has two interfaces and thus has two contact angles. It has been found that double interfaces cause resistance to displacement, and the resisting pressure rises while one contact angle increasing and the other decreasing during mobilization. To quantitatively explain how the resistance to flow builds up according to the contact angle variations during mobilization, it is assumed that (1) contact points remain unmoved; (2) the volume of a bubble or blob maintains constant; (3) once the interface starts moving at low capillary number, the contact angle remains to be the advancing or receding angle; (4) the viscous effect on pressure drop can be ignored; and (5) the two angles of two interfaces are equal to an equilibrium angle at the initiation of mobilization. A theoretical model is developed based on these assumptions, and the quantitative relationship of the two angles is expressed by an implicit function. Combining Young-Laplace equation, the capillary pressure induced by double interfaces is obtained. The model's prediction is in good agreement with experiments in studies. The equilibrium angle has strong influence on the variation of the two angles. When the equilibrium angle is less than 90 degrees, a relatively greater change in the contact angle at the advancing interface leads to a smaller change in the other one. Otherwise, the opposite is true. The changes of the two angles are equal when the equilibrium angle is 90 degrees. Moreover, a linear trend proposed by a previous investigation is incorporated into the model, to predict the ending of mobilization stage and to predict the maximum mobilization pressure on a given solid surface.