Ashish - not an easy question to answer. At the end of the day - and depending on your origin country - many different terms will be used to describe the same thing - especially health programmes. I rarely come across the terms mission or scheme - but regularly come across related terms such as health intervention, health education, health promotion etc - but it really does depend on many and multiple, complex contexts - hence not being able to supply specific citation or references.
The scheme is the model of something, reduced to its essential elements, the basis of which can subsequently be developed and completed. In this sense it is first of missions and programs.
The missions are the main functions and the strategic objectives pursued, using financial, human and material resources for those purposes.
The programs represent homogeneous groups of activities to achieve the defined objectives in missions.
From Indian context Mission like NHM is the ultimate/ desired long term health achievements that the country envision. Programs are a sub components of mission and look into a related groups of health issues and desire to achieve the respective goals and targets those put together can lead the country in its envisioned mission. Schemes are sub components of programmes with definitive objectives and targets. In short Mission is a mother set, that have multiple subsets i.e. programs and each program further subsets of schemes. But many times they are used interchangeably.