Microsoft seem to recommend that you use XMFLOAT4 and XMFLOAT4X4 to store the values, and use XMVECTOR and XMMATRIX for calculations.
From the DirectXMath help : (http://msdn.microsoft.com/en-us/library/windows/desktop/ee418725(v=vs.85).aspx#basic_usage)
"However, often it is easier and more compact to avoid using XMVECTOR or XMMATRIX directly in a class or structure. Instead, make use of the XMFLOAT3, XMFLOAT4, XMFLOAT4X3, XMFLOAT4X4, and so on, as members of your structure. Further, you can use the Vector Loading and Vector Storage functions to move the data efficiently into XMVECTOR or XMMATRIX local variables, perform computations, and store the results. There are also streaming functions (XMVector3TransformStream, XMVector4TransformStream, and so on) that efficiently operate directly on arrays of these data types."
You can store the XMVECTOR and XMMATRIX types but specially if you store them in vectors and so on it can be very hard to get the alignment requirements right as the default allocators don't meet the requirements.