Sometimes while reading a book aloud to my child I find myself thinking about something else, entirely different from that which I'm reading. I can do this so long as I'm not aware I'm doing it, because as soon as I realise I'm thinking about something else I can no longer read one thing and think another.
If I happen to hear two distinct pieces of music at the same time I can only pay attention to the structure of one at the expense of the other. In a similar way I cannot think about reading and be thinking something else simultaneously, I cannot consciously hold two distinct streams of thought. But this raises the question of whether I am aware am I thinking — or just thinking. I can be aware after the fact, by which time it is too late. There is the thinking, and the fact of my awareness of the thinking, which are distinct and incompatible trains of thought.
It seems to be a characteristic of consciousness that we can be aware of one stream of thought — one concatenation of meanings — at a time. However, this is by no means the same thing as a 'unity of mind.'