A lose reading of the DMG rules suggests that a Tiny Hut blocks the passage through the Ethereal Plane.

As divibisan's answer states, the DMG rules about movement in the Bordered Ethereal strongly implies that going in and out a Tiny Hut via the Ethereal plane is not possible.

Actually, the above ruling is a DM call.

Anyway, this is one possible interpretation of the rules, since the spell description does not say anything about blocking the passage in the Ethereal plane, while there are spells that specify this:

• Wall of Force (emphasis mine):

Nothing can physically pass through the wall. It is immune to all damage and can't be dispelled by dispel magic. A disintegrate spell destroys the wall instantly, however. The wall also extends into the Ethereal Plane, blocking ethereal travel through the wall.

• Forcecage\$^1\$ (emphasis mine):

A creature inside the cage can't leave it by nonmagical means. [...] The cage also extends into the Ethereal Plane, blocking ethereal travel.

\$^1\$ credits to Soulstreak for having pointed this out in the comments.

A lose reading of the DMG rules suggests that a Tiny Hut blocks the passage through the Ethereal Plane.

As divibisan's answer states, the DMG rules about movement in the Bordered Ethereal strongly implies that going in and out a Tiny Hut via the Ethereal plane is not possible.

Actually, the above ruling is a DM call.

Anyway, this is one possible interpretation of the rules, since the spell description does not say anything about blocking the passage in the Ethereal plane, while there are spells that specify this:

• Wall of Force (emphasis mine):

Nothing can physically pass through the wall. It is immune to all damage and can't be dispelled by dispel magic. A disintegrate spell destroys the wall instantly, however. The wall also extends into the Ethereal Plane, blocking ethereal travel through the wall.

• Forcecage\$^1\$ (emphasis mine):

A creature inside the cage can't leave it by nonmagical means. [...] The cage also extends into the Ethereal Plane, blocking ethereal travel.

\$^1\$ credits to Soulstreak for having pointed this out in the comments.

DMG rules strongly suggest a DM's ruling that does not allow the passage via the Ethereal Plane.

As divibisan's answer states, the DMG rules about movement in the Bordered Ethereal strongly implies that going in and out a Tiny Hut via the Ethereal plane is not possible.

Anyway, this is one possible interpretation of the rules, since the spell description does not say anything about blocking the passage in the Ethereal plane, while there is at least one spell, Wall of Force, that specifies this (emphasis mine):

Nothing can physically pass through the wall. It is immune to all damage and can't be dispelled by dispel magic. A disintegrate spell destroys the wall instantly, however. The wall also extends into the Ethereal Plane, blocking ethereal travel through the wall.

A lose reading of the DMG rules suggests that a Tiny Hut blocks the passage through the Ethereal Plane.

As divibisan's answer states, the DMG rules about movement in the Bordered Ethereal strongly implies that going in and out a Tiny Hut via the Ethereal plane is not possible.

Actually, the above ruling is a DM call.

Anyway, this is one possible interpretation of the rules, since the spell description does not say anything about blocking the passage in the Ethereal plane, while there are spells that specify this:

• Wall of Force (emphasis mine):

Nothing can physically pass through the wall. It is immune to all damage and can't be dispelled by dispel magic. A disintegrate spell destroys the wall instantly, however. The wall also extends into the Ethereal Plane, blocking ethereal travel through the wall.

• Forcecage\$^1\$ (emphasis mine):

A creature inside the cage can't leave it by nonmagical means. [...] The cage also extends into the Ethereal Plane, blocking ethereal travel.

\$^1\$ credits to Soulstreak for having pointed this out in the comments.