What would the ploidy of a multinucleate cell be?
Ploidy is generally defined in terms of the number of chromosomes in the nucleus, rather than the number of chromosomes in the cell. 

Some examples in support of this:
- A paramecium has a diploid micronucleus and polyploid macronucleus
- Muscle cells are generally considered diploid even though they have multiple nuclei
- The additional chromosomes in mitochondria and chloroplasts are not considered to make cells polyploid, even if the organelle itself may be polyploid.

Thus, I would assess a cell such as you describe to be haploid, albeit with two nuclei.