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There is absolutely no reason why a table cannot be used as a dimension table in one data mart and a fact table in another data mart. In practice we often design the dimension and fact tables so that they have only one function; which means that they are frequently used for only one purpose -- but that is more for our convenience than for anything else. So, what you are suggesting is fine.
In fact, we can go further. There is no reason why the value in a column of a table can't be both a measure and a dimensional member. Think about a value like "Number of Children."
If your analytical process asks for the average number of children that house buyers have (as opposed to people who rent) then you are using it as a measure. If you ask to see the average price paid for a house by those people with:
1
2
3
4
and
5
children respectively, then you are using the number of children to segment the data. So here, 'Price Paid' is the measure and 'Number of Children' is the dimension.
More about dimension and fact tables
Design recommendations for FACT TABLE and DIMENSIONS
Referencing a dimension table from a fact table
More about data marts
Data warehouse appliances go mainstream
Data mart vs. data warehouse
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