I just came accross this article:
Slate et al. 2004. Understanding the relationship between the inbreeding coefficient and multilocus heterozygosity: theoretical expectations and empirical data
Heredity (2004)93, 255–265. doi:10.1038/sj.hdy.6800485
And I was surprised to read in the abstract that:
"Multilocus heterozygosity was only weakly correlated with inbreeding coefficient, and heterozygosity was not positively correlated between markers more often than expected by chance. Inbreeding coefficient, but not multilocus heterozygosity, detected evidence of inbreeding depression for morphological traits"
Hmm. I am missing something ... I always thought this two measures should be correlated.