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Our studio has a one-hour TV program which runs three times a week and broadcasts different films. The content of the program is usually like the following, so can we call each broadcast an episode of the program?

1st broadcast: part one of a film

2nd broadcast: part two of the same film

3rd broadcast: part one of a new film

4th broadcast: part two of the new film

……

Does the word “episode” apply to each individual broadcast of a TV program, no matter what the content each time?

An episode is something that has a beginning and an end:

An episode is a coherent narrative unit within a larger dramatic work.

When an episode is too long to be aired in a single continuous broadcast, we are talking about a multi-part episode:

A multi-part episode is used when a given plot development is, quite simply, too big for one time slot.

See examples of usage here and here..

Note: your use of the term broadcast is potentially misleading. The same episode - or a part - can be broadcast (aired) many times.

The online Oxford dictionary of English offers the following definition of episode in the context of broadcasting.

2
Each of the separate instalments into which a serialized story or radio or television programme is divided.
‘the final episode of the series’

So the answer is ‘yes’. Broadcasting media have a ‘librarianship’, where programmes that are not one-off or daily are for reference purposes divided into ‘series’ and ‘episodes’. An ‘episode’ is a single broadcast made as part of a series.

We tend to think of it as part of a continuous drama. There is a good historical reason for this. The Greek theatre was divided into:

‘theatron’ (auditorium, though literally it means the place for watching);
‘orchestra’ (the circular place where choric dancing took place;
‘skini’ <σκηνή>, from which we get ‘scene’, which started out life as some sort of tent in which the actors could change, and on which the tragedian Sophocles first painted ‘scenery’.
‘eisodos’ or ‘entrance’ (one on each side) along which both chorus and actors could enter. So an ‘episode’ was a coming onto the scene, in which one or more actors advanced the plot.

That is how we got the word episode to mean a relatively self-contained portion of a serialised drama or novel.

That is where the confusion arises. The word ‘serial’ is well established for broadcasts like Eastenders or The Archers. But ‘series’ are something slightly different. In BBC IPlayer listings, these are identified by date of first broadcast. This is true of any daily or weekly broadcast, without a pre-determined last date.

Dramas and documentaries with a predetermined end point get listed by series number and episode number.

Confusing? Yes, a little. Serials without a predetermined last episode are catalogued by date. Serialised novels and dramas are listed by episode.

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Compare it to how the word is used in reference to talk shows and podcasts: the episodes of a podcast rarely have anything to do with eachother, but they are produced as a series, and that's what makes them episodes.

For a normal TV show, an episode is usually a part of the story that is broadcasted as a unit, and together span a narrative over a whole series.

In your TV show, if I understand it correctly, you focus on some certain type of film and broadcast a part of a film in each broadcast.

If you think of it in terms of broadcasting a single film in two parts, "episode" is a bit unnatural, but if you think of your show as an overarching concept covering many films, I think "episode" is fine. If it is meant as a series, the individual parts can be considered episodes.