If I manage to get a dropbar on my mtb and want to use both the MTB brake lever AND the road dropbar brake lever (like the Tiagra STI, but no gear shifting)... Is it possible? Can they use the same brake cable? I want something like
What you're looking for are called Cross or Interrupter levers (i.e. they interrupt the brake cable housing--the cable passes through them. It is worth noting that in the video the cables protruding from the sides of the brake hoods are shifter cables...the brake cable is routed under the handlebar tape to the cross levers).
Most setups are designed to work around short pull brakes (cantilevers, side pulls, &tc.). Long pull brakes (linear pull v-brakes, most mechanical disc brakes) require more cable to be pulled per motion of the brake levers, so it is generally not recommended to mix short and long pull components (though some report varying degrees of success).
If you have cantilever studs on your frame, you can easily find a set of cantilever brakes and a cross/drop lever combination that work well together. For long pull drop levers, there are fewer options (the ones that stick out in my mind are Cane Creek Drop Vs, and Tektro RL520s). For cross levers, there is only one that I've found that has a long pull option: Paul components makes a cross lever which can switch between short and long pull pivot location. (Alternatively, there are a few "mini" v-brakes which are short pull brakes.)
Your best option, given the availability of long pull road/cross levers, is to invest in something called a Travel Agent--it mounts to your v-brakes and effectively makes them short pull so that you can use any kind of road brake levers. They cost ~$20 each and are well worth it considering the headache of procuring compatible components or setting up cantilevers for the first time.
If you have mechanical disc brakes (which are generally long pull), you can either invest in long pull levers or switch to the Avid BB-7 Road calipers which are short pull and work quite well.
Additionally, pay attention to the diameter of the drop bar you'll be using and the levers you install! Most mountain bars have an OD of 22.2mm where road bars have an OD of 23.8mm.
Get Cane Creek Drop V levers for the drops. Standard Drop Bar levers have a shorter pull and you'll want ones that are compatible with V brakes longer pull (same issue if you're running MTB Disc brakes).
Then use your existing mtb brake levers for the tops of the bars, and get a pair of problem solvers cable doubler 2:1 to split the cables to work with two levers for a single brake.
Find a pair of Tektro RL740 cross levers which can pull v-brakes (again, longer pull than for canti/caliper or road disc) and use those instead of your mtb brakes. I'm not sure these are still available from tektro, but i saw a pair on ebay for about $25 USD.
Follow WTHarper's solution and use travel agents with short pull drop bar levers and regular cyclocross interrupter levers.