Is it possible for someone to be both depressed and bipolar?

Mixed bipolar: Yes, mixed affective episode is a prevalent mood disorder characterized by the coexistence or rapid alternation of manic and depressive symptoms, which is associated with significant suffering and high risk of suicide. Mixed bipolar states are associated with more severe symptoms and outcome. Fountoulakis et al2012 found that atypical antipsychotics such as queitaipine provides best response.

It Is Bipolar: If peole experience symptoms of bipolar disorder, then any depressive symptoms are considered to be part of that diagnosis. For example, you cannot be diagnosed with both bipolar disorder and major depression - bipolar disorder always subsumes a diagnosis of depression.