Given the limited information we (and maybe also you) have, it is statistically most likely that mental-health issues are the predominant reason for your husband’s suicide¹, and I will therefore at first assume this.
I may also make some further incorrect assumptions, which may seem somewhat imposing, but is just to avoid case distinctions, abstractions, etc.
I advise to consider such a suicide as the lethal symptom of a psychiatric disease, which is also in line with the modern medical point of view.
Such diseases can be notoriously hard to identify, in particular as many victims do not seek professional help or confide in others (which in turn may be another symptom of the disease or due to social stigma).
Moreover such diseases may be interacting with physiological ones; though I do not think that this should affect our attitude towards them.
From this point of view, your husband committed suicide because he was overwhelmed by this disease and not thinking straight.
The father your children knew would (probably) not have done this.
Taking this stance, the consideration that your he explicitly abandoned his family does not really arise – at least not much more as if he had died from, say, a sudden stroke.
The enemy was the disease, not your husband himself.
This is also the way I would communicate this to your children.
For example, a rough progression of accounts could be:
Your father suddenly got very sick, and he died because of it.
Your father had an illness of the brain that caused him to have absurd thoughts from time to time.
One of these thoughts was that it was a good idea to kill himself.
Sadly when he had that thought, nobody was around to stop him.
An elaboration of psychiatric diseases, how they make the victims suffer from depressions, psychoses, and similar, how these can lead to suicidal thoughts, how difficult they are to detect and treat, how difficult the victim’s state of mind is to grasp by other people, how your husband was likely affected by one of these diseases (and you probably do not know details), etc.
Mind that I would not consider or treat the first two points as lies.
They are not even a careful omission of facts.
They are just a reduction to what children at a certain age can understand – for the same reason they cannot understand a full physiological explanation of cancer.
And psychiatric diseases are extremely difficult to grasp, just going by how slowly humanity made progress at it so far.
Something similar applies to other reasons of suicide (though, given what you told us, it is hard to conceive one that has not at least a major psychiatric component):
Whatever caused the suicide is the enemy, not your husband.
For example, if your husband committed suicide because he was diagnosed with a terminal physiological disease, that disease is what you should be focusing on as a cause of death.
¹ For example, according to Surveillance for Violent Deaths — National Violent Death Reporting System, 16 States, 2008 (Table 7), at least 45% of suicide victims had a mental-health problem and 31% had problems with substance abuse (these do not seem to be fully included in the 45%, but may overlap with these), which I would also consider a mental-health problem for the purpose of this answer. I consider other prominent causes (relationship problems, life crisis, physical health, legal and financial problems) more unlikely than in the general population, given that you describe the suicide as sudden.