Software architecture is critical in succeeding with DevOps. However, designing software architectures that enable and support DevOps (DevOps-driven software architectures) is a challenge for organizations. We assert that one of the essential steps towards characterizing DevOps-driven architectures is to understand architectural design issues raised in DevOps. At the same time, some of the architectural issues that emerge in the DevOps context (and their corresponding architectural practices or tactics) may stem from the context (i.e., domain) and characteristics of software organizations. To this end, we conducted a mixed-methods study that consists of a qualitative case study of two teams in a company during their DevOps transformation and a content analysis of Stack Overflow and DevOps Stack Exchange posts to understand architectural design issues in DevOps. Our study found eight specific and contextual architectural design issues faced by the two teams and classified architectural design issues discussed in Stack Overflow and DevOps Stack Exchange into 11 groups. Our aggregated results reveal that the main characteristics of DevOps-driven architectures are: being loosely coupled and prioritizing deployability, testability, supportability, and modifiability over other quality attributes. Finally, we discuss some concrete implications for research and practice.