You want to connect short-pull levers with long-pull brakes. If done directly, this won't work effectively as you won't exert enough force on the brakes to stop you effectively.
More on pull lengths can be found in What is the actual cable pull of brake levers?
You need some mechanism to increase the pull length, either the one mentioned in the answer to this question: https://bicycles.stackexchange.com/a/59105/34697 or some DIY mechanism inspired by How much cable can I pull with a brake lever in another custom mechanism, and how can I achieve it? - if you trust your DIY skills.
If you want to retain your road brake levers, which are short-pull, and pull-length conversion contraption is not an option, you need to get yourself some short-pull brakes. These can either be cantilever brakes (you will make use of the currently available brake bosses) or find suitable (called long-reach) caliper brakes (or their center-pull version).
Both options (changing the brakes or installing the pull-length converter) will allow you to later replace the brake levers with some brifters (road bike brake levers integrated with the derailleur shifters).