Maybe would it be better in Life & Times Board.
The Militia Act of 1757 made enrolment compulsory for those selected by ballot.
I think estate owners were excepted (not sure) and one could, if unlucky with the ballot but rich, pay somebody to go instead.
But I think that if Mr Darcy had an estate in Derbyshire with 10.000£ of yearly income, this made of him the richest in the county after the Duke of Devonshire, and he could be expected to take responsibilities in the militia - not necessarily taking the regimentals...
Is it a "coincidence" that in 1795-1797, just when Jane Austen wrote "First Impressions", the Derbyshire Militia were encamped in Hertfordshire, and two brothers of hers, having responsabilities in Oxfordshire Militia, were in close relationship with officers of the Derbyshire Militia?
Little is said of any link between Darcy, Bingley and the Militia, but in chapter 7, the two friends are to dine with the officers. So one can fancy that they did something for this militia, without belonging to it.