Making a mixin of interfaces in Typescript

Yes you can, as of Typescript 1.6. Called Intersection types, use the & operator to combine types.

function extend<T, U>(first: T, second: U): T & U {
  let result = <T & U> {};
  for (let id in first) {
    result[id] = first[id];
  }

  for (let id in second) {
    if (!result.hasOwnProperty(id)) {
      result[id] = second[id];
    }
  }
  return result;
}

var x = extend({ a: "hello" }, { b: 42 });
x.a; // works
x.b; // works 

is there any way I can just put it as an "inline" mixin of interfaces inside the method parameter list

No. You cannot extend an interface inline