Either, the moon is tidally locked to the big planet, or it is tidally locked to the Sun, as it cannot be tidally locked to both. That is because that would require the moon to have the exact same orbital period as the big planet has around the star. That is not possible, except in the five special cases of the Lagrangian points, two of which are stable. As you are looking for a solution where both conditions can be true, I assume you are interested in these points:
L4 and L5 (the stable ones):
One hemisphere is always facing the star, which is the brightest light in the sky, and exactly 60 degrees away from the sun, a weaker light is the planet, looking like the Moon in its first quarter forever. Astronomers on this world can observe that the distance to the star, the big planet, and between the big planet and the star are exactly equal, forming a triangle. This may cause some strange views on orbital mechanics.
Boring. The planet is hidden behind the star, so the inhabitants of the world may think they are just on a regular planet.
One hemisphere is always illuminated by the star, and the opposite hemisphere by "planet light". What may be visible from the dark side is a small black dot on the big planet, caused by our world blocking some sunlight.
If the big planet has a low density, such as a gas giant, the L2 point lies inside the penumbra, causing an eternal solar eclipse and total darkness.
If the big planet has a higher density, the planet is only blocking some of the light from the star, causing a "ring of fire" in the sky.
Note however that none of these points are actually orbits around the planet, but rather border-case scenarios. The closest one can get to what you describe is having a Moon which orbit is tilted 90 degrees in relation to the orbit of the big planet, and combined with a tidal lock, both the big planet and the star appears to stay almost still in the sky, with the exception of the star making a full revolution for each of the big planet's orbits.