This paper investigates when an omnichannel brand should offer digital coupons in the online and buy-online-and-pick-up-in-store (BOPS) channels and, if so, the joint decision of coupon face value and store inventory. The impact of a digital coupon promotion on store inventory is also explored. Two scenarios are considered, one where consumers’ costs in the online and store channels are homogeneous and another in which they are heterogeneous, and two newsvendor models, with and without a coupon promotion, are constructed under each scenario. The results show that the issuance of coupons improves the omnichannel brand’s profit when the price is high and the coefficient of the difference in valuation between two types of consumers is low in the homogeneous scenario. In the heterogeneous scenario, the brand prefers the coupon promotion when the price is high or moderate and the coefficient of the difference in valuation between two types of consumers is high. In addition, offering a coupon promotion yields a higher store inventory in most cases. However, store inventory is decreased in some special cases in the homogeneous scenario. Moreover, an increased hassle cost in the BOPS channel significantly lowers the offline demand and profit increase from a digital coupon promotion. Furthermore, a coupon promotion is more likely to benefit both the brand and consumers as the cross-selling revenue increases. These results provide guidance for omnichannel brands to implement coupon promotions and adjust store inventory with stochastic demand.